How to solve the following problem?

This question was in the 1982 SAT, and was attempted wrong by each and everyone, just because the answer is not in the options!

To solve this problem, we have to look at the coin paradox, which can be actually solved by:-

1. First take two identical coins.

2. Stick one at a place, and rotate the other whilst the other one being stationary.

3. If properly observed, the coin completes exactly one rotation at the half of the other circle's circumference, and it actually completes two rotations to complete the other circle.

So, to actually solve this problem, we can let the circle start its own rotation, and see it completes one rotation at the quarter of the bigger circle, then at the next quarter, and so on! So total rotations required to cover the bigger circle = 4

But C1/C2 = 3, that is the ratio of both the circumference, should be the actual rate is moving isn't it?

This holds true if the frame of rotation is either one of the circles, that is only one of the two is actually seen moving. Then it is done in 1/3 of the bigger circle.

If the person who is testing this, is an external observer, the answer turns to be N+1, where N = perimeter of the circle.

This also actually very useful in the field of astronomy, as we on earth, consider a year to be 365.24 days, but a w.r.t a star, or any other celestial object, it is actually 366.24 days! This is also called Sidereal Time!

Thank you for reading this!